Theorems · Definition · category theory
HomologicalComplex.Hom.next
{ι : Type u_1} →
{V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
{c : ComplexShape ι} → {C₁ C₂ : HomologicalComplex V c} → C₁.Hom C₂ → (i : ι) → C₁.xNext i ⟶ C₂.xNext if.next i is f.f j if there is some r i j, and f.f j otherwise.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.Hom.fproof · cited by 845
- ComplexShape.nextproof · cited by 297
- HomologicalComplex.xNextstatement · cited by 28
- HomologicalComplex.Homstatement and proof · cited by 23
Cited by6
Results whose statement or proof uses this declaration.
- HomologicalComplex.Hom.sqFromproof · cited by 4
- HomologicalComplex.Hom.comm_fromstatement · cited by 2
- HomologicalComplex.Hom.next_eqstatement and proof · cited by 0
- HomologicalComplex.Hom.comm_from_applystatement and proof · cited by 0
- HomologicalComplex.Hom.comm_from_assocstatement and proof · cited by 0
- HomologicalComplex.Hom.sqFrom_rightstatement · cited by 0